Question

Answer the 32 question rightly and I'll mark it as brainliest.​

Answer 1

Answer:-

$given \: cos \: x = \frac{13}{14} and \: cos \: y \: = \frac{1}{7}$

$x \: and \: y \: are \: acute \: angles$

$sin \: x \: = \sqrt{1 - {cos}^{2} \: x }$

$= \sqrt{1 - \frac{169}{196} }$

$\sqrt{ \frac{27}{196} }$

$sin \: x \: = \frac{3 \sqrt{3} }{14}and \: sin \: y \: = \frac{4 \sqrt{3} }{7}$

$now \: cos \: (x - y) = cos \: x \: cos \: y \: + sin \: x \: sin \: y$

$\frac{13}{14} \times \frac{1}{7} + \frac{3 \sqrt{3} }{14} \times \frac{4 \sqrt{3} }{7}$

$= \frac{1}{2}$

$|x - y| = {cos}^{ - 1} \frac{1}{2} = \frac{\pi}{3}$

Now, we know cosθ is a decreasing function

and

13/14> 1/7

⇒cosx>cosy⇒x<y

⇒x−y<0

from (1)

−(x−y)= π / 3

⇒x−y= -π / 3. proved

hope it will help you.....